第八周任务一之复数类中运算符的重载

源程序：

方案一：用类的成员函数完成运算符的重载

/*(文件注释头部开始）
*程序的版权和版本声明部分
*Copyright (c) 2011,烟台大学计算机学院学生
*All rights reserved.
*文件名称：复数类运算符重载
*作    者：2011级计114-3张宗佳
*完成日期：2011年4月9号
*版本号：vc
* 对任务及求解方法的描述部分
* 输入描术：
* 问题描述：定义一个复数类重载运算符+、-、*、/，使之能用于复数的加减乘除。
* 程序输出：
* 程序头部的注释结束
*/
#include<iostream>

using namespace std;

class Complex
{
public:

Complex(){real = 0;imag = 0;}
Complex(double r,double i){real= r;imag = i;}

Complex operator + (Complex &c2);
Complex operator - (Complex &c2);
Complex operator * (Complex &c2);
Complex operator / (Complex &c2);

void display();

private:

double real;
double imag;
};
//下面定义成员函数
Complex Complex::operator + (Complex &c2)
{
return Complex(real + c2.real,imag + c2.imag);
}
Complex Complex::operator - (Complex &c2)
{
return Complex(real - c2.real,imag - c2.imag);
}
Complex Complex::operator * (Complex &c2)
{
return Complex(real * c2.real - imag * c2.imag, imag * c2.real + real * c2.imag);
}
Complex Complex::operator / (Complex &c2)
{
return Complex((real * c2.real + imag * c2.imag) / (c2.real * c2.real),(imag * c2.real - real * c2.imag) / (c2.imag * c2.imag));
}
void Complex::display()
{
cout << "(" << real << "," << imag << "i)" << endl;
}
int main()
{
Complex c1(3,4),c2(5,-10),c3;
cout<<"c1=";
c1.display();

cout<<"c2=";
c2.display();

c3=c1+c2;
cout<<"c1+c2=";
c3.display();

c3=c1-c2;
cout<<"c1-c2=";
c3.display();

c3=c1*c2;
cout<<"c1*c2=";
c3.display();

c3=c1/c2;
cout<<"c1/c2=";
c3.display();

system("pause");
return 0;
}

方案二：用类的友元函数，而不是成员函数完成运算符的重载

#include<iostream>

using namespace std;

class Complex
{
public:

Complex(){real = 0;imag = 0;}
Complex(double r,double i){real= r;imag = i;}

friend Complex operator + (Complex &c1,Complex &c2);
friend Complex operator - (Complex &c1,Complex &c2);
friend Complex operator * (Complex &c1,Complex &c2);
friend Complex operator / (Complex &c1,Complex &c2);

void display();

private:

double real;
double imag;
};
//下面定义成员函数
Complex operator + (Complex &c1,Complex &c2)
{
return Complex(c1.real + c2.real,c1.imag + c2.imag);
}
Complex operator - (Complex &c1,Complex &c2)
{
return Complex(c1.real - c2.real,c1.imag - c2.imag);
}
Complex operator * (Complex &c1,Complex &c2)
{
return Complex(c1.real * c2.real - c1.imag * c2.imag, c1.imag * c2.real + c1.real * c2.imag);
}
Complex operator / (Complex &c1,Complex &c2)
{
return Complex((c1.real * c2.real + c1.imag * c2.imag) / (c2.real * c2.real),(c1.imag * c2.real - c1.real * c2.imag) / (c2.imag * c2.imag));
}
void Complex::display()
{
cout << "(" << real << "," << imag << "i)" << endl;
}
int main()
{
Complex c1(3,4),c2(5,-10),c3;
cout<<"c1=";
c1.display();

cout<<"c2=";
c2.display();

c3=c1+c2;
cout<<"c1+c2=";
c3.display();

c3=c1-c2;
cout<<"c1-c2=";
c3.display();

c3=c1*c2;
cout<<"c1*c2=";
c3.display();

c3=c1/c2;
cout<<"c1/c2=";
c3.display();

system("pause");
return 0;
}

 

实验结果：



方案三：在方案二的基础上，扩展+、-、*、/运算符的功能，使之能与double型数据进行运算。设Complex c; double d; c?d和d?c的结果为将d视为实部为d的复数同c运算的结果（其中?为+、-、*、/之一）。另外，定义一目运算符-，-c相当于0-c。

#include<iostream>

using namespace std;

class Complex
{
public:

Complex(){real = 0;imag = 0;}
Complex(double r,double i){real= r;imag = i;}

Complex operator + (double &i);
Complex operator - (double &i);
Complex operator * (double &i);
Complex operator / (double &i);

friend Complex operator + (double &i,Complex &c2);
friend Complex operator - (double &i,Complex &c2);
friend Complex operator * (double &i,Complex &c2);
friend Complex operator / (double &i,Complex &c2);
Complex operator - ();//声明一目运算符 -

void display();

private:

double real;
double imag;
};
//下面定义成员函数
Complex Complex::operator + (double &i)
{
return Complex(i + real, imag);
}
Complex Complex::operator - (double &i)
{
return Complex(i - real, imag);
}
Complex Complex::operator * (double &i)
{
return Complex(i * real, i * imag);
}
Complex Complex::operator / (double &i)
{
return Complex((i * real ) / (real * real),(i * imag) / (imag * imag));
}
Complex operator + (double &i,Complex &c2)
{
return Complex(i + c2.real, c2.imag);
}
Complex operator - (double &i,Complex &c2)
{
return Complex(i - c2.real, c2.imag);
}
Complex operator * (double &i,Complex &c2)
{
return Complex(i * c2.real, i * c2.imag);
}
Complex operator / (double &i,Complex &c2)
{
return Complex((i * c2.real ) / (c2.real * c2.real),(i * c2.imag) / (c2.imag * c2.imag));
}
Complex Complex::operator - ()//定义一目运算符 -
{
return Complex(-real,-imag);//以相反数的形式返回
}
void Complex::display()
{
cout << "(" << real << "," << imag << "i)" << endl;
}
int main()
{
Complex c1(3,4),c3;

double i = 3;

cout<<"c1=";
c1.display();

c3 = c1 + i;

cout << "c1+3=";

c3.display();

c3 = i + c1;
cout << "3+c1=";
c3.display();

c3 = c1 * i;

cout << "c1-3=";

c3.display();

c3 = i * c1;
cout << "3-c1=";
c3.display();
c3 = c1 + i;

cout << "c1*3=";

c3.display();

c3 = i + c1;
cout << "3*c1=";
c3.display();
c3 = c1 + i;

cout << "c1/3=";

c3.display();

c3 = i + c1;
cout << "3/c1=";
c3.display();

c3 = -c1;
cout << "-c1=";
c3.display();

system("pause");
return 0;
}

实验结果：



经验积累：

1.在定义类的友元函数时，要定义两个参数

2.要实现实数与复数的交换律，可以定义一个成员函数和一个友元函数，但是友元函数中的第一个参数必须是实数

3.还要注意复数的乘法与除法法则！

上机感言：

为了复数之间的相乘和相除捣鼓了半天，终于算出来了...